Convergence Analysis for a Finite Element Approximation of a Steady Model for Electrorheological Fluids

TL;DR

This paper analyzes the convergence of finite element methods applied to a variable exponent p(·)-Stokes model for electrorheological fluids, providing error estimates for velocity and pressure approximations.

Contribution

It offers new convergence analysis and error estimates for finite element approximations of a variable exponent p(·)-Stokes system, which models electrorheological fluids.

Findings

Derived optimal error estimates for velocity and pressure

Established convergence results in suitable functional settings

Provided theoretical foundations for numerical simulations of electrorheological fluids

Abstract

In this paper we study the finite element approximation of systems of $p(\cdot)$-Stokes type, where $p(\cdot)$ is a (non constant) given function of the space variables. We derive --in some cases optimal-- error estimates for finite element approximation of the velocity and of the pressure, in a suitable functional setting.